A basis for discussion: what is truth?
Mmm ... riding on Kant's coattails, I will just add that this sort of problems becomes easier if you distinguish between analytical truths, that are implied in definitions and synthetical truths, which are not.
To clarify matters, let's look at some truths:
"a square has four equal sides" is analytical, because a square is defined as a parallelogram with four equal sides. Of course, you could define a square as my uncle Pedro after he has drunk a bottle of mezcal and before he has fallen on the floor, and then you would be at liberty to claim that a square has many more sides than four.
This is entirely within your rights, but you still are within the analytical truths.
"One plus one equals two" can be proved true. This particular sentence reminds us that it is necessary to check whether we and the interlocutor share certain basic axioms. In binary, for example, 1+1=10.
"The sun rises outside your house in the morning": or, more appropriately, it has risen every morning up to today. If the sun were to go nova tonight, then the sentence would probably be wrong. This would be a kind of statystical truth, but not analytical (nothing in the definition of the Sun forces it to rise every morning).
"cigarettes cause cancer" "the US contains no tropical islands" are synthetic truths (and thus subject to revision). These truths are indeed subjective (and temporary), I am afraid. What if it turned out that it is not the cigarette smoke that kills you, but rather the vapors from the cigarette filter ? And what if Puerto Rico became a US state ?
So, is truth subjective?
One would say that synthetic truths are quite subjective, while analytical truths are objective --- ooh, maybe objectiveish, but this becomes a large, devastatingly complex topic. Useful references to continue in the discussion: truth, intensional, extensional, truth value, boolean logic, Bertrand Russell, Benjamin Pierce.